Below is a listing of the types of pets that Hunters can tame. All information collected from ThottBot.

Type Damage Armor Health Diet Skills
Bat +7%     Fruit, Fungus Bite, Dive, Screech
Bear -9% +5% +8% Bread, Cheese, Fish, Fruit, Fungus, Meat Bite, Claw
Boar -10% +9% +4% Bread, Cheese, Fish, Fruit, Fungus, Meat Bite, Charge, Dash, Gore
Carrion Bird   +5%   Fish, Meat Bite, Claw, Dive, Screech
Cat +10%   -2% Fish, Meat Bite, Claw, Dash, Prowl
Crab -5% +13% -4% Bread, Fish, Fruit, Fungus Claw
Crocolisk   +10% -5% Fish, Meat Bite
Dragonhawk       Fish, Fruit, Meat Bite, Dive, Fire Breath
Gorilla +2%   +4% Fruit, Fungus Bite, Thunder Stomp
Hyena   +5%   Fruit, Meat Bite, Dash
Nether Ray +3% -10% +10% Meat Bite, Dive
Owl +7%     Meat Claw, Dive, Screech
Raptor +10% +3% -5% Meat Bite, Claw
Ravager +10% +5% -7% Meat Bite, Dash, Gore
Scorpid -6% +10%   Meat Claw, Scorpid Poison
Serpent       Fish, Meat Bite, Poison Spit
Spider +7%     Meat Bite
Sporebat       Bread, Cheese, Fruit, Fungus  
Tallstrider     +5% Cheese, Fruit, Fungus Bite, Dash
Turtle -10% +13%   Fish, Fruit, Fungus Bite, Shell Shield
Warp Stalker -6% +5%   Fish, Fruit Bite, Claw, Warp
Wind Serpent +7%     Bread, Cheese, Fish Bite, Dive, Lightning Breath
Wolf   +5%   Meat Bite, Dash, Furious Howl